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hktoc

a guest Sep 25th, 2017 49 Never
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  1. Linear Equations
  2.     Fields
  3.     Systems of Linear Equations
  4.     Matrices & elementary row operations
  5.     Row-reduced Echelon Matrices
  6.     Matrix Multiplication
  7.     Invertible Matrices
  8.  
  9. Vector Spaces
  10.     Vector Spaces
  11.     Subspaces
  12.     Bases and Dimension
  13.     Coordinates
  14.     Summary of Row-Equivalence
  15.     Computations Concerning Subspaces
  16.  
  17. Linear Transformations
  18.     Linear Transformations
  19.     The Algebra of Linear Transformations
  20.     Isomorphism
  21.     Representations of Transformations by Matrices
  22.     Linear Functionals
  23.     The Double Dual
  24.     The Transpose of a Linear Transformation
  25.  
  26. Polynomials
  27.     Algebras
  28.     The Algebra of Polynomials
  29.     Lagrange Interpolation
  30.     Polynomial Ideals
  31.     The Prime Factorization of a Polynomial
  32.  
  33. Determinants
  34.     Commutative Rings
  35.     Determinant Functions
  36.     Permutations and Uniqueness of Determinants
  37.     Additional Properties of Determinants
  38.     Modules
  39.     Multilinear Functions
  40.     The Grassman Ring
  41.  
  42. Elementary Canonical Forms
  43.     Introduction
  44.     Characteristic Values
  45.     Annihilating Polynomials
  46.     Invariant Subspaces
  47.     Simultaneous Triangulation; Simultaneous Diagonalization
  48.     Direct-sum Decompositions
  49.     Invariant Direct Sums
  50.     The Primary Decomposition Theorem
  51.  
  52. The Rational and Jordan Forms
  53.     Cyclic Subspaces and Annihilators
  54.     Cyclic Decompositions and the Rational Form
  55.     The Jordan Form
  56.     Computation of Invariant Factors
  57.     Summary; Semi-Simple Operators
  58.  
  59. Inner Product Spaces
  60.     Inner Products
  61.     Inner Product Spaces
  62.     Linear Functionals and Adjoints
  63.     Unitary Operators
  64.     Normal Operators
  65.  
  66. Operators on Inner Product Spaces
  67.     Introduction
  68.     Forms on Inner Product Spaces
  69.     Positive Forms
  70.     More on Forms
  71.     Spectral Theory
  72.     Further Properties of Normal Operators
  73.  
  74. Bilinear Forms
  75.     Bilinear Forms
  76.     Symmetric Bilinear Forms
  77.     Skew-Symmetric Bilinear Forms
  78.     Groups Preserving Bilinear Forms
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